Finding the Derivative?

[Hanajima]

Hey guys, could anyone help, me with these problems?

a. f(t)= (t^2-9) ?t+2

b. y= ?x(x-2)^2

c. y= t^2 ?t-2

d. f(x) = x+1/ 2x-3

Step by Step explanations on how you arrived at your answers would be great.
Please and thank you!

For A, I got an answer of 5t^2-8t / 2? t-2, but I'm not sure if that's right.
We just started chain rules, product rules, quotient rules, etc in class today and I'm just so confused when and which rule to use.

 

[BigGlenntheHeavy]

\(\displaystyle For \ a \ you \ have \ f(x) \ = \ (t^{2}-9)\sqrt t+2 \ = \ t^{5/2}-9t^{1/2}+2\)

\(\displaystyle f \ ' \ (x) \ = \ \bigg(\frac{5}{2}\bigg)t^{3/2}-9\bigg(\frac{1}{2}\bigg)t^{-1/2}+0 \ = \ \frac{5t^{2}+9}{2t^{1/2}}\)